Deep surrounding rock anchor rod spacing quantitative determination method based on fracture toughness parameter

Abstract

The invention discloses a deep surrounding rock anchor rod spacing quantitative determination method based on fracture toughness parameters. The method comprises the following steps: obtaining the fracture toughness and uniaxial compressive strength of rock through an indoor test; determining a uniaxial compression parameter and an elastic modulus of the rock mass by combining a geological strength index GSI, a damage factor D and a Hoek-Brown criterion; calculating a brittleness index B4 by using the fracture toughness of the surrounding rock, the uniaxial compressive parameter of the rock mass and the elastic modulus; and based on the brittleness index B4, the rock mass elasticity modulus, the engineering burial depth and the rock mass volume weight, a quantitative calculation formula of the anchor rod spacing is established, an empirical coefficient is solved in combination with the spacing range of the corresponding surrounding rock grade in the specification, and finally quantitative determination of the anchor rod spacing is achieved. The method overcomes the defect that quantitative basis is lacked in spacing adjustment in existing specifications, and is particularly suitable for anchor rod support design for controlling brittle failure of surrounding rocks under the deep high-stress condition.

Description

Technical Field

[0001] This invention belongs to the field of underground engineering support design technology in geotechnical engineering, specifically relating to a quantitative design method for anchor bolt support parameters for deep underground engineering, and in particular a method for determining anchor bolt spacing based on the fracture toughness and brittleness index of the surrounding rock. Background Technology

[0002] In the support design of deep underground engineering projects (such as mine roadways, traffic tunnels, and hydraulic tunnels), rock bolt support is one of the key technical means to control the stability of the surrounding rock. The spacing of the rock bolts, as a core parameter in support design, directly affects the safety and economy of the project.

[0003] Currently, several domestic standards and specifications (such as the "Engineering Rock Mass Classification Standard" (GB / T 50218-2014), the "Highway Tunnel Design Specification" (JTG D70-2018), and the "Water Conservancy and Hydropower Engineering Anchor-Sprayed Support Technical Specification" (SL377-2007)) provide guidance for the design of anchor bolt spacing. These specifications typically provide an empirical range of spacing values ​​based on the surrounding rock grade, combined with factors such as the development of rock mass structural surfaces and tunnel span, for designers to refer to and adjust.

[0004] However, this empirical method based on surrounding rock classification has significant limitations. First, the given spacing adjustment range is usually large, lacking precise quantitative adjustment basis, and relies heavily on the designer's experience and judgment, thus exhibiting a degree of subjectivity. Second, and more importantly, the failure mode of surrounding rock in deep, high-stress underground engineering differs fundamentally from that in shallow engineering. Under high ground stress, deep surrounding rock is more prone to stress-driven brittle failure, manifesting as dynamic phenomena such as rock bursts, spalling, and block ejection. In this case, the main purpose of support is not to control large plastic deformation, but to suppress the fragmentation of the surrounding rock and the sudden release of energy. Furthermore, there is no necessary connection between traditional surrounding rock classification and the inherent brittle failure tendency of the rock mass. For example, hard sandstone with well-developed joints, although classified as Class III medium surrounding rock due to structural planes, is still brittle in its rock material itself and is highly susceptible to brittle tensile cracking or block collapse under high stress; conversely, relatively intact weak rock strata (such as some argillaceous limestone) may exhibit more plastic deformation characteristics. Clearly, the surrounding rock grade alone cannot accurately reflect and control the risk of brittle failure in deep surrounding rocks.

[0005] To quantitatively describe the brittleness of rocks, the academic community has proposed several brittleness indices that include fracture toughness. For example: index This method characterizes brittleness by comparing fracture toughness and elastic strain energy, providing a clear physical meaning, but it does not directly include information about plastic deformation; (Indicators) It correlates well with the brittle transition point in indentation tests, but is not sensitive to the plastic deformation of macroscopic engineering rock masses; (Indicators) While the calculations are simple, they neglect the crucial role of material stiffness in stress transfer and energy storage, resulting in limited accuracy. Although these indicators represent theoretical progress and provide a physical basis for brittleness assessment, they still share common problems: most focus on the properties of the rock material itself, failing to fully consider the macroscopic mechanical behavior of the engineering rock mass under the influence of structural surfaces and excavation disturbances (such as rock mass strength and deformation modulus); more importantly, they have not yet established a direct and quantitative mathematical connection with anchor bolt support design parameters (especially spacing), making them unsuitable for direct application in engineering design.

[0006] Therefore, existing standardized methods and academic indicators are insufficient to meet the refined and quantitative requirements of anchor bolt support design in deep underground engineering. There is an urgent need to establish a quantitative method for determining anchor bolt spacing that is directly related to the brittle failure tendency of the surrounding rock, comprehensively considers rock mass mechanical parameters, and has a clear engineering application path. This would compensate for the shortcomings of existing technologies and provide a more scientific and reliable theoretical basis for anchor bolt support design under deep, high-risk geological conditions. Summary of the Invention

[0007] To address the above technical problems, this invention proposes a method for quantitatively determining the spacing of anchor bolts in deep surrounding rock based on fracture toughness parameters. This method first uses indoor testing to obtain the fracture toughness of the target lithology of the formation, then obtains the fracture toughness of the surrounding rock in the engineering area based on the formation conditions, obtains the brittleness index of the surrounding rock in the anchor bolt design area based on the fracture toughness of the surrounding rock, and then quantitatively solves the anchor bolt design spacing based on the brittleness index of the surrounding rock.

[0008] A method for quantitatively determining the spacing of anchor bolts in deep surrounding rock based on fracture toughness parameters, specifically including: S1. Obtain the uniaxial compressive strength of the target formation rock through indoor testing. ), elastic modulus ( ) and fracture toughness ( ); S2. Determine the rock mass mechanical parameters of the surrounding rock in the engineering area: S2.1: Determine the surrounding rock grade based on the on-site geological log, and obtain the range of values ​​for the geological strength index GSI by referring to the table; calculate the damage factor D of the rock mass through acoustic wave testing of the surrounding rock excavated on-site and intact rock blocks indoors; S2.2: The uniaxial compressive strength ( Substituting the GSI value range and damage factor D into the Hoek-Brown criterion, the uniaxial compressive strength of the rock mass is calculated. ) and rock mass elastic modulus ( The upper and lower limits of ); S2.3: Based on the fracture toughness ( The range of GSI values ​​is determined by the formula. Estimate the effective fracture toughness of the surrounding rock mass ( The upper and lower limits of ), where m is the empirical index to be determined; S3, Calculate the brittleness index of the surrounding rock ( ): Based on the fracture toughness of the rock mass ( ), rock mass elastic modulus ( ) and uniaxial compressive strength of rock mass ( ), through formula Calculate the brittleness index ( The upper and lower limits of ). S4. Quantitatively determine the anchor bolt design spacing (S): S4.1: Establish the anchor spacing calculation model, the formula is as follows: Where k is an undetermined empirical coefficient. For the unit weight of the rock mass, To increase the depth of the project; and Substituting the upper and lower limit expressions, we obtain the upper and lower limit expressions for the anchor spacing (S) containing unknown coefficients m and k; S4.2: Based on the surrounding rock grade, refer to the design specifications to obtain the corresponding recommended anchor bolt spacing range; solve the calculated upper and lower limit expressions of anchor bolt spacing with the recommended range in the specifications to calculate the values ​​of empirical coefficients m and k. S4.3: Determine the single GSI value of the target surrounding rock area based on detailed geological data. Using the obtained coefficients m and k, repeat steps S2.2 to S4.1 to calculate the final quantitative anchor bolt design spacing (S).

[0009] Further, in step S1, the fracture toughness ( The elastic modulus () was obtained through the Brazilian disc test; It was obtained through an indoor uniaxial compression test.

[0010] Further, in step S2.1, the formula for calculating the damage factor D is: in, The longitudinal wave velocity of the rock mass was measured on-site after excavation. The longitudinal wave velocity is the value of the complete rock block in the laboratory test.

[0011] Further, in step S2.2, the uniaxial compressive strength of the rock mass ( ) and rock mass elastic modulus ( ) is calculated using the following formula: Among them, rock mass material constants and The calculation formula is: Furthermore, in step S4.2, the value of the empirical index m ranges from 0.5 to 1; while the value of the empirical coefficient k ranges from 0.5 to 1.2.

[0012] Furthermore, in step S4.3, the determination of the specific GSI single value of the target surrounding rock area is achieved through an improved GSI quantification system method, a GSIw downgrading method, or a method based on the number of joints in the rock mass.

[0013] Compared with the prior art, the beneficial effects of the present invention are: 1. This invention establishes a calculation model based on fracture toughness and brittleness indices, transforming the determination of anchor bolt spacing from a qualitative range selection dependent on surrounding rock grade and engineering experience to a quantitative mathematical calculation based on rock mechanics parameters. This significantly reduces subjectivity in the design process and improves the accuracy and scientific rigor of the design.

[0014] 2. This invention directly addresses the core problem of brittle failure in deep, high-stress surrounding rock. The fracture toughness parameters used can effectively describe the material's ability to resist crack instability and propagation, and the brittleness index derived therefrom can more accurately reflect the inherent tendency of the surrounding rock to undergo brittle failures such as rock bursts and spalling.

[0015] 3. This invention provides a complete and operable implementation path. This method does not use the fracture toughness of rock materials in isolation, but introduces parameters such as geological strength index (GSI) and damage factor (D) to reasonably transform rock material parameters (laboratory scale) into engineering rock mass parameters (engineering scale), and finally directly associates them with the engineering design parameter of anchor spacing, thus solving the problem of the disconnect between laboratory indicators and macroscopic engineering design.

[0016] 4. This invention fully considers the heterogeneity and uncertainty of the engineering rock mass. By using the upper and lower limits of GSI for derivation, a quantitative range of anchor spacing considering the fluctuation range of geological conditions is finally obtained, rather than a single fixed value. This makes the design results more robust and reliable, and can adapt to the complex and ever-changing geological conditions of deep engineering. Attached Figure Description

[0017] Figure 1 This is an overall flowchart of the present invention; Figure 2 The diagram shows the geometry and loading of the SCB specimen. R is the specimen radius, B is the thickness, a is the notch length, s is the distance between the two supporting cylindrical rollers, and P is the monotonically increasing compressive load applied to the central loading roller during three-point bending loading. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention.

[0019] Example This invention provides a method for quantitatively determining the spacing of anchor bolts in deep surrounding rock based on fracture toughness parameters, specifically including the following steps: Step 1: Obtain basic mechanical parameters of rocks through indoor tests The basic mechanical parameters of intact rock core samples from the target strata were obtained through laboratory testing methods, including: uniaxial compressive strength of the rock. In accordance with the "Standard for Test Methods of Engineering Rock Mass" (GB / T 50266) and other specifications, standard indoor uniaxial compression tests of rock were conducted to obtain the uniaxial compressive strength of the rock. Rock fracture toughness Using macroscopic testing methods recommended by the International Society for Rock Mechanics (ISRM) and other organizations, and considering the heterogeneity and structural characteristics of the rock, the Type I fracture toughness of the rock was obtained. The commonly used method is the Brazilian disc test (DOI 10.1007 / s00603-013-0422-7): The rock core sample to be tested is prepared as follows: Figure 2 The semi-disc specimen shown has a central crack. A central notch is introduced into the semi-disc specimen on its horizontal side. Two supporting cylindrical rollers are symmetrically arranged below the horizontal side of the semi-disc specimen. A radial load is applied downwards towards the notch from the arch of the semi-disc specimen. The rock fracture toughness is calculated using the formula: -1.297+9516(s / 2R)-(0.47+16.457(s / 2R))β+(1.071+34.401(s / 2R))β 2 β≥0.2 in, The radius of the semi-circular specimen is 1. Let be the thickness of the semi-disc specimen, and P be the observed peak load. The length of the gap. β is a dimensionless stress intensity factor. .

[0020] Step 2: Determine the rock mass mechanical parameters of the surrounding rock in the engineering area. This step aims to transform the complete rock parameters measured in the laboratory into rock mechanics parameters that can reflect the quality and damage state of the rock mass at the engineering site.

[0021] Step 2.1: Determine the Geological Strength Index (GSI) and Damage Factor (D): A. Based on the on-site geological logging, determine the surrounding rock grade and geological strength index (GSI) of the target project area: According to the current "Engineering Rock Mass Classification Standard" (GB / T 50218), the basic quality (BQ) of rock mass characterizes the most fundamental property inherent in the rock mass that affects the stability of engineering rock mass. It is determined by both the hardness of the intact rock block and the integrity of the jointed rock mass. The calculation formula is as follows: In the formula, Rc is the saturated uniaxial compressive strength of intact rock, and Kv is the rock integrity index. The longitudinal wave velocity of the surrounding rock after excavation was obtained through on-site acoustic wave testing. The values ​​were obtained from on-site tests after excavation, and the longitudinal wave velocity of the intact rock block was obtained through indoor ultrasonic testing. ), which represents the indoor test values ​​of the complete rock block.

[0022] There is a strong linear positive correlation between the BQ value defined by the national standard and the RMR value in the international rock mass engineering community. The regression equation can be expressed as: Hoek, Kaiser, and Brown established the relationship between GSI and RMR values: RMR = 15lg(10) Vpm-3.5 When RMR > 23, GSI = RMR − 5; B. Referring to the five rock mass quality levels of the BQ system in the "GB / T50218 Engineering Rock Mass Classification Standard", as shown in Table 1, find the GSI value range (upper limit and lower limit) corresponding to the surrounding rock grade, and obtain the table of correspondence between surrounding rock grade and GSI.

[0023] According to the formula The damage factor D of the rock mass was calculated.

[0024] Table 1 Correspondence between Surrounding Rock Grade and GSI Step 2.2: Calculate the uniaxial compressive strength of the rock mass ( ) and rock mass elastic modulus ( ): The uniaxial compressive strength of the rock obtained in step 1 ( The GSI value range and damage factor D determined in step 2.1 are substituted into the relevant formula of the Hoek-Brown criterion (Hoek E, Carranza–Torres C, Corkum B. Hoek–Brown failure criterion-2002 edition[J]. In: Proceedings of the NARMS-TAC conference, Toronto, 2002, (1): 267-273) to calculate the uniaxial compressive strength of the rock mass. ) and rock mass elastic modulus ( The upper and lower limits of ) In the formula, and Rock mass material constants: Note: The above This represents the uniaxial compressive strength of intact rock obtained through laboratory testing (i.e., a complete, continuous rock specimen, at the laboratory scale), while This represents the uniaxial compressive strength of the engineering rock mass estimated using the Hoek-Brown criterion (i.e., the on-site engineering rock mass including structural surfaces such as joints and fissures, which is an engineering scale).

[0025] Step 2.3: Estimate the effective fracture toughness of the rock mass ( ): Based on the intact rock fracture toughness obtained in step 1 ( The effective fracture toughness of the rock mass in the engineering area was estimated using an empirical reduction method based on the Geological Strength Index (GSI). The more fractured the rock mass, the greater the decrease in its effective fracture toughness compared to intact rock. The calculation formula is: Where m is an empirical index to be determined (usually between 0.5 and 1). Substituting the upper and lower limits of GSI into the equation (refer to Table 1), the effective fracture toughness of the rock mass containing the unknown m can be obtained. The upper and lower bound expressions of ).

[0026] Step 3: Calculate the brittleness index of the surrounding rock (B4) The fracture mechanics-based brittleness index B4 is used to quantitatively characterize the brittle failure tendency of the surrounding rock, where a smaller B4 value indicates greater brittleness. The effective fracture toughness of the rock mass obtained in step 2.3 (…) ), rock mass elastic modulus ( ) and uniaxial compressive strength of rock mass ( Substitute into the following formula: This yields the upper and lower limits of the brittleness index of the surrounding rock containing the unknown m.

[0027] Step 4: Quantitatively determine the anchor bolt design spacing (S) Step 4.1: Establish the anchor spacing calculation model: The anchor spacing (S) is determined by the elastic modulus of the rock mass. brittleness index The depth of the burial site and the unit weight of the rock mass are jointly determined. The calculation formula is as follows: in, The empirical coefficient is to be determined (usually between 0.5 and 1.2); The elastic modulus of the rock mass obtained in step 2; The brittleness index obtained in step 3; The unit weight of the rock mass; The depth of the engineering area.

[0028] Will and After substituting the upper and lower limit values, the upper and lower limit values ​​of the anchor spacing S are finally obtained.

[0029] Step 4.2, Solve for the empirical coefficients (m and k): Based on the surrounding rock grade of the target project area, consult the current relevant design specifications to find the recommended range of anchor bolt spacing values ​​corresponding to this grade of surrounding rock, as shown in Table 2.

[0030] Table 2 Based on the upper limit of the anchor spacing calculated in step 3, which is equal to the upper limit of the specification, and the lower limit of the anchor spacing, which is equal to the lower limit of the specification, the specific values ​​of the two key empirical coefficients m and k are calculated.

[0031] Step 4.3: Calculate the final design spacing: After obtaining the empirical coefficients m and k, return to step 2.1. Based on more accurate geological data, an improved GSI quantification system method, the GSIw downgrading method, or the rock mass volume joint number (Jv) method can be used to determine a more specific single GSI value for the surrounding rock in the engineering area.

[0032] The three methods are as follows: ①Based on the volumetric joint number of the rock mass ( The method: In the formula, This represents the total number of joints contained in each cubic meter of rock mass. , , , This represents the number of joints that the survey line passes through in each group; , , , k is the average spacing (meters) of each joint group; k' is the number of joint groups.

[0033] in Quantitative relationship with rock mass structure (vertical axis): Calculate The corresponding "structural rating" in the GSI chart can be determined by looking up a table or using an empirical formula.

[0034] Table 3 Empirical formula: For well-structured rock masses, GSI and The relationship can be approximated as: (Among them, the "structural score" part of RMR is related to...) (Related) ② An improved GSI quantification system, which identifies two quantitative parameters: rock mass structure score (F) and joint surface condition score (C). The rock mass structure score corresponds to the vertical axis and is determined by the number of joints in the rock mass volume. It is determined together with the number of joint groups.

[0035] First according to Determine the structural coefficient r: For blocky structures, r = 0.15 +0.85; for fragmented structures, r=0.10 +1.10; For extremely fragmented / scattered structures, r=0.05 +1.10. Then, based on the number of joint groups and the structural coefficient r, refer to the table below to obtain the structural score: Table 4 The joint surface score (C) corresponds to the horizontal axis, and the parameter C is determined by three factors: C1 represents the roughness coefficient, determined by the roughness of the joint surface. Specifically, C1 = 1.0 for a rough, wavy joint surface; C1 = 0.85 for a smooth, wavy joint surface; C1 = 0.70 for a rough, straight joint surface; C1 = 0.50 for a smooth, straight joint surface; and C1 = 0.30 for a mirror-like joint surface with scratches. C2 represents the weathering coefficient. Specifically, C2 = 1.0 for an unweathered joint surface; C2 = 0.85 for a slightly weathered joint surface; C2 = 0.65 for a moderately weathered joint surface; C2 = 0.45 for a strongly weathered joint surface; and C2 = 0.25 for a completely weathered joint surface. C3 represents the infill coefficient. When the joint surface is unfilled and closed, C3 = 1.0; when the hard infill material (such as quartz) of the joint surface is < 5 mm, C3 = 0.90; when the soft infill material (such as clay) of the joint surface is < 5 mm, C3 = 0.60; when the infill material thickness of the joint surface is > 5 mm, C3 = 0.20-0.40.

[0036] final Calculation formula: ③GSIw downgrading method: This method considers GSI as a process of gradual "downgrading" starting from a complete rock matrix (GSI=100) and progressing with the development of structural planes and deterioration of conditions. In the formula, This indicates a matrix that is intact but weak. For weak rocks, it is usually not 100, but may be set to 85 or 90. The total degradation score is composed of two parts: structural degradation and surface condition degradation.

[0037] The specific calculation steps are as follows: a Based on rock mass volume joint number Obtain the structural degradation score (SD). when <1, SD=0; when 1 < <3.75, SD=8 ( -1); when 3.75 < <10, SD=5 ( +5); when 10 < <40, SD=3 ( +15); when >40, SD=165 (maximum value).

[0038] b. Based on a deduction table for surface roughness, weathering degree, and infill condition, obtain the surface condition degrading score (SCD). For example, smooth and straight joints have an SCD score of 15; moderately weathered joints have an SCD score of 10; joints containing clay fillers have an SCD score of 20-40... c calculates the total demotion score and : final The value is limited to between 0 and 100.

[0039] Using the specific GSI value calculated by any of the above methods, repeat steps 2 and 3 to obtain a set of determined rock mass elastic moduli. ) and fragility index ( ).

[0040] Finally, the confirmed , Rock mass unit weight burial depth and the coefficients that have been obtained Substituting the values ​​into the spacing formula from step 4.1, the final, quantitative anchor bolt design spacing S is calculated. Alternatively, based on the project's safety level, a reasonable safety margin can be taken near the calculated value as the final design value.

[0041] For example: 1. Basic mechanical parameters of the rock were obtained through indoor tests. The uniaxial compressive strength of the granite was 250 MPa, the elastic modulus was 70 GPa, and the fracture toughness was 2.08 MN / m. 3 / 2 .

[0042] 2. Based on the on-site geological data, the surrounding rock category is Class III. Referring to the table, the upper limit of the GSI is determined to be 50, and the lower limit is 35. The measured wave velocity of the rock mass on-site is 4500 km / s, while the wave velocity of intact rock in the laboratory is 5600 km / s. Therefore, according to the formula... The calculated damage factor of the rock mass is D=0.35.

[0043] 3. Uniaxial compressive strength of rock mass ( ) and rock mass elastic modulus ( Find the upper and lower limits of GSI respectively: Take the upper limit GSI=50, Take the lower limit GSI=35, 4. Effective fracture toughness of rock mass ( Find the upper and lower limits of GSI respectively: Take the upper limit GSI=50: Take the lower limit GSI=35: 5. Calculate the brittleness index of the surrounding rock (B4) Take the upper limit GSI=50: Take the lower limit GSI=35: 6. Based on the on-site engineering depth of 1200m and the unit weight of granite of 26.8 kN / m³, 3 The anchor bolt spacing is calculated with respect to the upper and lower limits of GSI: Take the upper limit GSI=50: Take the lower limit GSI=35: Solving the system of equations simultaneously yields: , 7. The improved GSI quantification system method adopted is based on the volume joint number ( The rock mass structure is scored based on the rock mass dimensions and the joint surface roughness. ), degree of alteration / filling of joint surfaces ( ) and the degree of weathering of the rock blocks ( The fracture surface condition is scored. Details are as follows: Joint number The structural coefficient of the blocky rock mass Therefore, the structural score is obtained. .

[0044] The joint surfaces of the surrounding rock at the site are rough and straight, slightly weathered, and without filling material, belonging to hard structural surfaces. Therefore, the roughness coefficient is obtained. Weathering coefficient Filler coefficient .

[0045] Therefore, we can calculate: Repeat steps S2.2 to S4.1 to calculate the final quantitative anchor bolt design spacing S = 1.36m. This yields an accurate recommended anchor bolt spacing value.

[0046] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for quantitatively determining the spacing of anchor bolts in deep surrounding rock based on fracture toughness parameters, characterized in that, Includes the following steps: S1. Obtain the uniaxial compressive strength of the target formation rock through indoor tests. Elastic modulus and fracture toughness ; S2. Determine the rock mass mechanical parameters of the surrounding rock in the engineering area: S2.1: Determine the surrounding rock grade based on the on-site geological log, and obtain the range of values ​​for the geological strength index GSI by referring to the table; calculate the damage factor D of the rock mass through acoustic wave testing of the surrounding rock excavated on-site and intact rock blocks indoors; S2.2: The uniaxial compressive strength Substituting the GSI value range and damage factor D into the Hoek-Brown criterion, the uniaxial compressive strength of the rock mass is calculated. and rock mass elastic modulus The upper and lower limits; S2.3: Based on the fracture toughness The range of GSI values ​​is determined by the formula. Estimate the effective fracture toughness of the surrounding rock mass The upper and lower limits, where m is the empirical index to be determined; S3. Calculate the brittleness index of the surrounding rock. : Based on the effective fracture toughness of the rock mass Rock mass elastic modulus Uniaxial compressive strength of rock mass Through formula Calculate brittleness index The upper and lower limits; S4. Quantitatively determine the anchor bolt design spacing S: S4.1: Establish the anchor spacing calculation model, the formula is as follows: Where k is an undetermined empirical coefficient. For the unit weight of the rock mass, To increase the depth of the project; and Substituting the upper and lower limit expressions, we obtain the upper and lower limit expressions for the anchor spacing S containing unknown coefficients m and k; S4.2: Based on the surrounding rock grade, refer to the design specifications to obtain the corresponding recommended anchor bolt spacing range; solve the calculated upper and lower limit expressions of anchor bolt spacing with the recommended range in the specifications to calculate the values ​​of empirical coefficients m and k. S4.3: Determine the single GSI value of the target surrounding rock area based on detailed geological data. Using the obtained coefficients m and k, repeat steps S2.2 to S4.1 to calculate the final quantitative anchor bolt design spacing S.

2. The method according to claim 1, characterized in that, In step S1, the fracture toughness The elastic modulus was obtained through the Brazilian disc test; Obtained through indoor uniaxial compression testing.

3. The method according to claim 1, characterized in that, In step S2.1, the formula for calculating the damage factor D is: in, The longitudinal wave velocity of the rock mass was measured on-site after excavation. The longitudinal wave velocity is the value of the complete rock block in the laboratory test.

4. The method according to claim 1, characterized in that, In step S2.2, the uniaxial compressive strength of the rock mass and rock mass elastic modulus Calculated using the following formula: Among them, rock mass material constants and The calculation formula is: 。 5. The method according to claim 1, characterized in that, In step S4.2, the value of the empirical index m ranges from 0.5 to 1; while the value of the empirical coefficient k ranges from 0.5 to 1.

2.

6. The method according to claim 1, characterized in that, In step S4.3, the determination of the specific GSI single value of the target surrounding rock area is achieved through an improved GSI quantification system method, a GSIw downgrading method, or a method based on the number of joints in the rock mass.

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